I have heard that some people prefer not to for tznius reasons. We see this in the Torah when Yaakov would travel with his family, his wives would travel in the back and when Eisav would travel his wives would go before him. So, how could it be that Eisav respects his wives more than Yaakov?
A medrash brings down that Yaakov Avinu was doing it out of respect for his wives. It’s not tznius for a man to walk behind a woman and watch her walk. So maybe some people feel that opening a door for a girl on a date (like a car door) is not tznius as he will watch the girl get out and walk before him…
Personally, I think its should be done and it’s rude not to.